%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU211+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:58:30 AM UTC 2026
% Result : Theorem 264.15s 264.41s
% Output : Proof 265.46s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(cc1_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('theBenchmark.p',cc1_relat_1) ).
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d14_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) ) ) ) ),
file('theBenchmark.p',d14_relat_1) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(dt_k10_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k10_relat_1) ).
fof(dt_k1_tarski,axiom,
$true,
file('theBenchmark.p',dt_k1_tarski) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_k2_tarski,axiom,
$true,
file('theBenchmark.p',dt_k2_tarski) ).
fof(dt_k4_tarski,axiom,
$true,
file('theBenchmark.p',dt_k4_tarski) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc1_zfmisc_1,axiom,
! [A,B] : ~ empty(ordered_pair(A,B)),
file('theBenchmark.p',fc1_zfmisc_1) ).
fof(fc2_subset_1,axiom,
! [A] : ~ empty(singleton(A)),
file('theBenchmark.p',fc2_subset_1) ).
fof(fc3_subset_1,axiom,
! [A,B] : ~ empty(unordered_pair(A,B)),
file('theBenchmark.p',fc3_subset_1) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(rc1_relat_1,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('theBenchmark.p',rc1_relat_1) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_relat_1,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('theBenchmark.p',rc2_relat_1) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t178_relat_1,conjecture,
! [A,B,C] :
( relation(C)
=> ( subset(A,B)
=> subset(relation_inverse_image(C,A),relation_inverse_image(C,B)) ) ),
file('theBenchmark.p',t178_relat_1) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_2_2,plain,
! [U_2] :
( relation(U_2)
| ~ empty(U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( relation(U_2)
| ~ empty(U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_3_2,plain,
! [U_4,U_3] : unordered_pair(U_4,U_3) = unordered_pair(U_3,U_4),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
unordered_pair(U_4,U_3) = unordered_pair(U_3,U_4),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A] :
( ! [B,C] :
( ( C = relation_inverse_image(A,B)
| ? [D] :
( ( ~ in(D,C)
& ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) ) )
| ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) ) )
& ( ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d14_relat_1]) ).
fof(f_4_2,plain,
! [U_13] :
( ! [U_12,U_11] :
( ( U_11 = relation_inverse_image(U_13,U_12)
| ? [U_10] :
( ( ~ in(U_10,U_11)
& ? [U_9] :
( in(U_9,U_12)
& in(ordered_pair(U_10,U_9),U_13) ) )
| ( ! [U_8] :
( ~ in(U_8,U_12)
| ~ in(ordered_pair(U_10,U_8),U_13) )
& in(U_10,U_11) ) ) )
& ( ! [U_7] :
( ( in(U_7,U_11)
| ! [U_6] :
( ~ in(U_6,U_12)
| ~ in(ordered_pair(U_7,U_6),U_13) ) )
& ( ? [U_5] :
( in(U_5,U_12)
& in(ordered_pair(U_7,U_5),U_13) )
| ~ in(U_7,U_11) ) )
| U_11 != relation_inverse_image(U_13,U_12) ) )
| ~ relation(U_13) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_13] :
( ( ! [U_21,U_19] :
( U_19 = relation_inverse_image(U_13,U_21)
| ? [U_17] :
( ~ in(U_17,U_19)
& ? [U_9] :
( in(U_9,U_21)
& in(ordered_pair(U_17,U_9),U_13) ) )
| ? [U_16] :
( ! [U_8] :
( ~ in(U_8,U_21)
| ~ in(ordered_pair(U_16,U_8),U_13) )
& in(U_16,U_19) ) )
& ! [U_20,U_18] :
( ( ! [U_15] :
( in(U_15,U_18)
| ! [U_6] :
( ~ in(U_6,U_20)
| ~ in(ordered_pair(U_15,U_6),U_13) ) )
& ! [U_14] :
( ? [U_5] :
( in(U_5,U_20)
& in(ordered_pair(U_14,U_5),U_13) )
| ~ in(U_14,U_18) ) )
| U_18 != relation_inverse_image(U_13,U_20) ) )
| ~ relation(U_13) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
! [U_13] :
( ( ! [U_21,U_19] :
( U_19 = relation_inverse_image(U_13,U_21)
| ? [U_17] :
( ~ in(U_17,U_19)
& ? [U_9] :
( in(U_9,U_21)
& in(ordered_pair(U_17,U_9),U_13) ) )
| ? [U_16] :
( ! [U_8] :
( ~ in(U_8,U_21)
| ~ in(ordered_pair(U_16,U_8),U_13) )
& in(U_16,U_19) ) )
& ! [U_20,U_18] :
( ( ! [U_15] :
( in(U_15,U_18)
| ! [U_6] :
( ~ in(U_6,U_20)
| ~ in(ordered_pair(U_15,U_6),U_13) ) )
& ! [U_14] :
( ( in(sK1(U_13,U_20,U_18,U_14),U_20)
& in(ordered_pair(U_14,sK1(U_13,U_20,U_18,U_14)),U_13) )
| ~ in(U_14,U_18) ) )
| U_18 != relation_inverse_image(U_13,U_20) ) )
| ~ relation(U_13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_5,sK1(U_13,U_20,U_18,U_14))],[f_4_3]) ).
fof(f_4_5,plain,
! [U_13] :
( ( ! [U_21,U_19] :
( U_19 = relation_inverse_image(U_13,U_21)
| ? [U_17] :
( ~ in(U_17,U_19)
& ? [U_9] :
( in(U_9,U_21)
& in(ordered_pair(U_17,U_9),U_13) ) )
| ( ! [U_8] :
( ~ in(U_8,U_21)
| ~ in(ordered_pair(sK2(U_13,U_21,U_19),U_8),U_13) )
& in(sK2(U_13,U_21,U_19),U_19) ) )
& ! [U_20,U_18] :
( ( ! [U_15] :
( in(U_15,U_18)
| ! [U_6] :
( ~ in(U_6,U_20)
| ~ in(ordered_pair(U_15,U_6),U_13) ) )
& ! [U_14] :
( ( in(sK1(U_13,U_20,U_18,U_14),U_20)
& in(ordered_pair(U_14,sK1(U_13,U_20,U_18,U_14)),U_13) )
| ~ in(U_14,U_18) ) )
| U_18 != relation_inverse_image(U_13,U_20) ) )
| ~ relation(U_13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_16,sK2(U_13,U_21,U_19))],[f_4_4]) ).
fof(f_4_6,plain,
! [U_13] :
( ( ! [U_21,U_19] :
( U_19 = relation_inverse_image(U_13,U_21)
| ( ~ in(sK3(U_13,U_21,U_19),U_19)
& ? [U_9] :
( in(U_9,U_21)
& in(ordered_pair(sK3(U_13,U_21,U_19),U_9),U_13) ) )
| ( ! [U_8] :
( ~ in(U_8,U_21)
| ~ in(ordered_pair(sK2(U_13,U_21,U_19),U_8),U_13) )
& in(sK2(U_13,U_21,U_19),U_19) ) )
& ! [U_20,U_18] :
( ( ! [U_15] :
( in(U_15,U_18)
| ! [U_6] :
( ~ in(U_6,U_20)
| ~ in(ordered_pair(U_15,U_6),U_13) ) )
& ! [U_14] :
( ( in(sK1(U_13,U_20,U_18,U_14),U_20)
& in(ordered_pair(U_14,sK1(U_13,U_20,U_18,U_14)),U_13) )
| ~ in(U_14,U_18) ) )
| U_18 != relation_inverse_image(U_13,U_20) ) )
| ~ relation(U_13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_17,sK3(U_13,U_21,U_19))],[f_4_5]) ).
fof(f_4_7,plain,
! [U_13] :
( ( ! [U_21,U_19] :
( U_19 = relation_inverse_image(U_13,U_21)
| ( ~ in(sK3(U_13,U_21,U_19),U_19)
& in(sK4(U_13,U_21,U_19),U_21)
& in(ordered_pair(sK3(U_13,U_21,U_19),sK4(U_13,U_21,U_19)),U_13) )
| ( ! [U_8] :
( ~ in(U_8,U_21)
| ~ in(ordered_pair(sK2(U_13,U_21,U_19),U_8),U_13) )
& in(sK2(U_13,U_21,U_19),U_19) ) )
& ! [U_20,U_18] :
( ( ! [U_15] :
( in(U_15,U_18)
| ! [U_6] :
( ~ in(U_6,U_20)
| ~ in(ordered_pair(U_15,U_6),U_13) ) )
& ! [U_14] :
( ( in(sK1(U_13,U_20,U_18,U_14),U_20)
& in(ordered_pair(U_14,sK1(U_13,U_20,U_18,U_14)),U_13) )
| ~ in(U_14,U_18) ) )
| U_18 != relation_inverse_image(U_13,U_20) ) )
| ~ relation(U_13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_9,sK4(U_13,U_21,U_19))],[f_4_6]) ).
cnf(f_4_8,plain,
( in(ordered_pair(U_14,sK1(U_13,U_20,U_18,U_14)),U_13)
| ~ in(U_14,U_18)
| U_18 != relation_inverse_image(U_13,U_20)
| ~ relation(U_13) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_9,plain,
( in(sK1(U_13,U_20,U_18,U_14),U_20)
| ~ in(U_14,U_18)
| U_18 != relation_inverse_image(U_13,U_20)
| ~ relation(U_13) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_10,plain,
( in(U_15,U_18)
| ~ in(U_6,U_20)
| ~ in(ordered_pair(U_15,U_6),U_13)
| U_18 != relation_inverse_image(U_13,U_20)
| ~ relation(U_13) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_11,plain,
( in(ordered_pair(sK3(U_13,U_21,U_19),sK4(U_13,U_21,U_19)),U_13)
| in(sK2(U_13,U_21,U_19),U_19)
| U_19 = relation_inverse_image(U_13,U_21)
| ~ relation(U_13) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_12,plain,
( in(sK4(U_13,U_21,U_19),U_21)
| in(sK2(U_13,U_21,U_19),U_19)
| U_19 = relation_inverse_image(U_13,U_21)
| ~ relation(U_13) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_13,plain,
( ~ in(sK3(U_13,U_21,U_19),U_19)
| in(sK2(U_13,U_21,U_19),U_19)
| U_19 = relation_inverse_image(U_13,U_21)
| ~ relation(U_13) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_14,plain,
( in(ordered_pair(sK3(U_13,U_21,U_19),sK4(U_13,U_21,U_19)),U_13)
| ~ in(U_8,U_21)
| ~ in(ordered_pair(sK2(U_13,U_21,U_19),U_8),U_13)
| U_19 = relation_inverse_image(U_13,U_21)
| ~ relation(U_13) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_15,plain,
( in(sK4(U_13,U_21,U_19),U_21)
| ~ in(U_8,U_21)
| ~ in(ordered_pair(sK2(U_13,U_21,U_19),U_8),U_13)
| U_19 = relation_inverse_image(U_13,U_21)
| ~ relation(U_13) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_16,plain,
( ~ in(sK3(U_13,U_21,U_19),U_19)
| ~ in(U_8,U_21)
| ~ in(ordered_pair(sK2(U_13,U_21,U_19),U_8),U_13)
| U_19 = relation_inverse_image(U_13,U_21)
| ~ relation(U_13) ),
inference(clausify,[status(thm)],[f_4_7]) ).
fof(f_5_1,plain,
! [A,B] :
( ( subset(A,B)
| ? [C] :
( ~ in(C,B)
& in(C,A) ) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(f_5_2,plain,
! [U_25,U_24] :
( ( subset(U_25,U_24)
| ? [U_23] :
( ~ in(U_23,U_24)
& in(U_23,U_25) ) )
& ( ! [U_22] :
( in(U_22,U_24)
| ~ in(U_22,U_25) )
| ~ subset(U_25,U_24) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_29,U_27] :
( subset(U_29,U_27)
| ? [U_23] :
( ~ in(U_23,U_27)
& in(U_23,U_29) ) )
& ! [U_28,U_26] :
( ! [U_22] :
( in(U_22,U_26)
| ~ in(U_22,U_28) )
| ~ subset(U_28,U_26) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_29,U_27] :
( subset(U_29,U_27)
| ( ~ in(sK5(U_29,U_27),U_27)
& in(sK5(U_29,U_27),U_29) ) )
& ! [U_28,U_26] :
( ! [U_22] :
( in(U_22,U_26)
| ~ in(U_22,U_28) )
| ~ subset(U_28,U_26) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_23,sK5(U_29,U_27))],[f_5_3]) ).
cnf(f_5_5,plain,
( in(U_22,U_26)
| ~ in(U_22,U_28)
| ~ subset(U_28,U_26) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_6,plain,
( in(sK5(U_29,U_27),U_29)
| subset(U_29,U_27) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_7,plain,
( ~ in(sK5(U_29,U_27),U_27)
| subset(U_29,U_27) ),
inference(clausify,[status(thm)],[f_5_4]) ).
fof(f_6_1,plain,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(fof_nnf,[status(thm)],[d5_tarski]) ).
fof(f_6_2,plain,
! [U_31,U_30] : ordered_pair(U_31,U_30) = unordered_pair(unordered_pair(U_31,U_30),singleton(U_31)),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
ordered_pair(U_31,U_30) = unordered_pair(unordered_pair(U_31,U_30),singleton(U_31)),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k10_relat_1]) ).
cnf(f_7_2,plain,
$true,
inference(clausify,[status(thm)],[f_7_1]) ).
fof(f_8_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
cnf(f_8_2,plain,
$true,
inference(clausify,[status(thm)],[f_8_1]) ).
fof(f_9_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_9_2,plain,
$true,
inference(clausify,[status(thm)],[f_9_1]) ).
fof(f_10_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_10_2,plain,
$true,
inference(clausify,[status(thm)],[f_10_1]) ).
fof(f_11_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
cnf(f_11_2,plain,
$true,
inference(clausify,[status(thm)],[f_11_1]) ).
fof(f_12_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
cnf(f_12_2,plain,
$true,
inference(clausify,[status(thm)],[f_12_1]) ).
fof(f_13_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_13_2,plain,
$true,
inference(clausify,[status(thm)],[f_13_1]) ).
fof(f_14_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_14_2,plain,
! [U_33] :
? [U_32] : element(U_32,U_33),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_33] : element(sK6(U_33),U_33),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_32,sK6(U_33))],[f_14_2]) ).
cnf(f_14_4,plain,
element(sK6(U_33),U_33),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_15_2,plain,
! [U_34] : ~ empty(powerset(U_34)),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
~ empty(powerset(U_34)),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_16_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_16_1]) ).
fof(f_17_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_17_2,plain,
! [U_36,U_35] : ~ empty(ordered_pair(U_36,U_35)),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
~ empty(ordered_pair(U_36,U_35)),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_18_2,plain,
! [U_37] : ~ empty(singleton(U_37)),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
~ empty(singleton(U_37)),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_19_2,plain,
! [U_39,U_38] : ~ empty(unordered_pair(U_39,U_38)),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
~ empty(unordered_pair(U_39,U_38)),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_20_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_20_1]) ).
fof(f_21_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_21_2,plain,
? [U_40] :
( relation(U_40)
& empty(U_40) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( relation(sK7)
& empty(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_40,sK7)],[f_21_2]) ).
cnf(f_21_4,plain,
empty(sK7),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
relation(sK7),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_22_2,plain,
! [U_42] :
( ? [U_41] :
( ~ empty(U_41)
& element(U_41,powerset(U_42)) )
| empty(U_42) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_42] :
( ( ~ empty(sK8(U_42))
& element(sK8(U_42),powerset(U_42)) )
| empty(U_42) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_41,sK8(U_42))],[f_22_2]) ).
cnf(f_22_4,plain,
( element(sK8(U_42),powerset(U_42))
| empty(U_42) ),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_5,plain,
( ~ empty(sK8(U_42))
| empty(U_42) ),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_23_2,plain,
? [U_43] : empty(U_43),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
empty(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_43,sK9)],[f_23_2]) ).
cnf(f_23_4,plain,
empty(sK9),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_24_2,plain,
? [U_44] :
( relation(U_44)
& ~ empty(U_44) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( relation(sK10)
& ~ empty(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_44,sK10)],[f_24_2]) ).
cnf(f_24_4,plain,
~ empty(sK10),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
relation(sK10),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_25_2,plain,
! [U_46] :
? [U_45] :
( empty(U_45)
& element(U_45,powerset(U_46)) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_46] :
( empty(sK11(U_46))
& element(sK11(U_46),powerset(U_46)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_45,sK11(U_46))],[f_25_2]) ).
cnf(f_25_4,plain,
element(sK11(U_46),powerset(U_46)),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
empty(sK11(U_46)),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_26_2,plain,
? [U_47] : ~ empty(U_47),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
~ empty(sK12),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_47,sK12)],[f_26_2]) ).
cnf(f_26_4,plain,
~ empty(sK12),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_27_2,plain,
! [U_49,U_48] : subset(U_49,U_49),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_49] : subset(U_49,U_49),
inference(miniscope,[status(thm)],[f_27_2]) ).
cnf(f_27_4,plain,
subset(U_49,U_49),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> ( subset(A,B)
=> subset(relation_inverse_image(C,A),relation_inverse_image(C,B)) ) ),
inference(negate,[status(cth)],[t178_relat_1]) ).
fof(f_28_2,negated_conjecture,
? [A,B,C] :
( ~ subset(relation_inverse_image(C,A),relation_inverse_image(C,B))
& subset(A,B)
& relation(C) ),
inference(fof_nnf,[status(thm)],[f_28_1]) ).
fof(f_28_3,negated_conjecture,
? [U_52,U_51,U_50] :
( ~ subset(relation_inverse_image(U_50,U_52),relation_inverse_image(U_50,U_51))
& subset(U_52,U_51)
& relation(U_50) ),
inference(variable_rename,[status(thm)],[f_28_2]) ).
fof(f_28_4,negated_conjecture,
? [U_51,U_50] :
( ~ subset(relation_inverse_image(U_50,sK13),relation_inverse_image(U_50,U_51))
& subset(sK13,U_51)
& relation(U_50) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_52,sK13)],[f_28_3]) ).
fof(f_28_5,negated_conjecture,
? [U_50] :
( ~ subset(relation_inverse_image(U_50,sK13),relation_inverse_image(U_50,sK14))
& subset(sK13,sK14)
& relation(U_50) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_51,sK14)],[f_28_4]) ).
fof(f_28_6,negated_conjecture,
( ~ subset(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))
& subset(sK13,sK14)
& relation(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_50,sK15)],[f_28_5]) ).
cnf(f_28_7,negated_conjecture,
relation(sK15),
inference(clausify,[status(thm)],[f_28_6]) ).
cnf(f_28_8,negated_conjecture,
subset(sK13,sK14),
inference(clausify,[status(thm)],[f_28_6]) ).
cnf(f_28_9,negated_conjecture,
~ subset(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)),
inference(clausify,[status(thm)],[f_28_6]) ).
fof(f_29_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_29_2,plain,
! [U_54,U_53] :
( element(U_54,U_53)
| ~ in(U_54,U_53) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( element(U_54,U_53)
| ~ in(U_54,U_53) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_30_2,plain,
! [U_56,U_55] :
( in(U_56,U_55)
| empty(U_55)
| ~ element(U_56,U_55) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( in(U_56,U_55)
| empty(U_55)
| ~ element(U_56,U_55) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
! [A,B] :
( ( element(A,powerset(B))
| ~ subset(A,B) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(fof_nnf,[status(thm)],[t3_subset]) ).
fof(f_31_2,plain,
! [U_58,U_57] :
( ( element(U_58,powerset(U_57))
| ~ subset(U_58,U_57) )
& ( subset(U_58,U_57)
| ~ element(U_58,powerset(U_57)) ) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( ! [U_62,U_60] :
( element(U_62,powerset(U_60))
| ~ subset(U_62,U_60) )
& ! [U_61,U_59] :
( subset(U_61,U_59)
| ~ element(U_61,powerset(U_59)) ) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
cnf(f_31_4,plain,
( subset(U_61,U_59)
| ~ element(U_61,powerset(U_59)) ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_5,plain,
( element(U_62,powerset(U_60))
| ~ subset(U_62,U_60) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_32_2,plain,
! [U_65,U_64,U_63] :
( element(U_65,U_63)
| ~ element(U_64,powerset(U_63))
| ~ in(U_65,U_64) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( element(U_65,U_63)
| ~ element(U_64,powerset(U_63))
| ~ in(U_65,U_64) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_33_2,plain,
! [U_68,U_67,U_66] :
( ~ empty(U_66)
| ~ element(U_67,powerset(U_66))
| ~ in(U_68,U_67) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_68,U_67] :
( ! [U_66] :
( ~ empty(U_66)
| ~ element(U_67,powerset(U_66)) )
| ~ in(U_68,U_67) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
cnf(f_33_4,plain,
( ~ empty(U_66)
| ~ element(U_67,powerset(U_66))
| ~ in(U_68,U_67) ),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_34_2,plain,
! [U_69] :
( U_69 = empty_set
| ~ empty(U_69) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( U_69 = empty_set
| ~ empty(U_69) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_35_2,plain,
! [U_71,U_70] :
( ~ empty(U_70)
| ~ in(U_71,U_70) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
( ~ empty(U_70)
| ~ in(U_71,U_70) ),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_36_2,plain,
! [U_73,U_72] :
( ~ empty(U_72)
| U_73 = U_72
| ~ empty(U_73) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_73] :
( ! [U_72] :
( ~ empty(U_72)
| U_73 = U_72 )
| ~ empty(U_73) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
( ~ empty(U_72)
| U_73 = U_72
| ~ empty(U_73) ),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_7_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_2]) ).
cnf(f_8_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_2]) ).
cnf(f_9_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_2]) ).
cnf(f_10_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_2]) ).
cnf(f_11_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_2]) ).
cnf(f_12_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_12_2]) ).
cnf(f_13_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_13_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( unordered_pair(Eq_x_0,Eq_x_1) = unordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( relation_inverse_image(Eq_x_0,Eq_x_1) = relation_inverse_image(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( ordered_pair(Eq_x_0,Eq_x_1) = ordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK2(Eq_x_0,Eq_x_1,Eq_x_2) = sK2(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK3(Eq_x_0,Eq_x_1,Eq_x_2) = sK3(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK4(Eq_x_0,Eq_x_1,Eq_x_2) = sK4(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK5(Eq_x_0,Eq_x_1) = sK5(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK6(Eq_x_0) = sK6(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( in(Eq_y_0,Eq_y_1)
| ~ in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,axiom,
( subset(Eq_y_0,Eq_y_1)
| ~ subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( element(Eq_y_0,Eq_y_1)
| ~ element(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU211+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 23:31:22 UTC 2026
% 0.09/0.37 % CPUTime :
% 264.15/264.41 % SZS status Theorem for theBenchmark
% 264.15/264.41 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------